Questions on the mathematical aspects of signal processing. Please consider first if your question might be more suitable for http://dsp.stackexchange.com/

learn more… | top users | synonyms (1)

0
votes
0answers
5 views

Frequency response of causal linear invariant systems.

So for linear causal invariant systems the $g(k)$ response is $g(k)=0$ for $k<0$ How about the frequency response? Since $G(f)=g(k)e^{-2j\pi f}$ then $G(f)=0$ for $f<0$?
1
vote
1answer
52 views

Series of $\csc(x)$ or $(\sin(x))^{-1}$

In some cases I found that $$\csc(x)= \lim\limits_{k\rightarrow \infty}\sum_{n=-k}^{k}(-1)^{n}\frac{1}{x-n\pi}$$ Is anything to prove or disprove that?
1
vote
1answer
844 views

Calculate phase and amplitude of a sampled sine wave

I have an electronics project where I sample two sine waves. I would like to know what the amplitude (peak) and difference in phase is. Actually I just need to know the average product of the two ...
0
votes
1answer
35 views

Expected value of product of sinusoids

In the book Adaptive Signal Processing by Widrow, an equation (2.20) on page 23 is presented without proof as: $$E \left[ x_k x_{k-n} \right] = \frac{1}{N} \sum_{k=1} ^{N} \sin\left(\frac{2 ...
2
votes
2answers
726 views

Approximate a polynomial function using a sum of sine waves

I have a polynomial function which I need to approximate by a sum of sine waves with constant amplitude along a given domain. From what I hear, this might be a good time to make use of Fourier ...
0
votes
0answers
16 views

Variance of estimating coefficients by correlating a sequence

I have a sequence $$ r[n] = a_1.t_1[n] + a_2.t_2[n] + a_3.t_3[n] + ... $$ where $t_1, t_2, t_3,...$ are uncorrelated, two-level (+A/-A), zero mean, pseudo-random sequences. To estimate $a_1$, ...
0
votes
1answer
23 views

Signal processing very short question?

We have $Y(k)=x(k-1)+ kx(k-5)+x(k)^4$ .I have to find the impulse response for the function So I know that $G(z) = \frac{Y(z)}{X(z)}$ but how do I relate that to this? $Y(z)=(z^{-1}) + k(z^{-5})+ ...
0
votes
0answers
24 views

Fourier kernels relations to windowing in signal processing.

In engineering a common practice is to "window" a signal (by multiplying a function which decays smoothly at each end) before applying a Fourier transform. Windowing is done to avoid false frequency ...
0
votes
0answers
32 views

What are the name of these signals

It might be funny but there are two signals which confuse me about how to call them. Signal1: http://s3.postimg.org/ffefhwqyr/Capture1.png Signal2: http://s3.postimg.org/samf4o683/Capture2.png I am ...
0
votes
0answers
20 views

Decompose summation of signals

Imagine a summation of three distinct signals such as in the following graphic. Is it possible to estimate the original signals? Below is a matlab-code to generate the image: I have found similar ...
0
votes
2answers
1k views

Undecimated Wavelet Transform (a trous algorithm) - how to determine 'anchor'/'center' of convolution filter

i am currently implementing the 'Undecimated Wavelet Transform' with the 'a trous' algorithm. See e.g. http://www.znu.ac.ir/data/members/fazli_saeid/DIP/Paper/ISSUE2/04060954_2.pdf, section II-A. As ...
0
votes
0answers
12 views

Are steady-state values in LTI systems differentially influenced by the rate an input is introduced? [migrated]

I have a general question about LTI systems I was hoping someone could clarify. I'm currently learning about steady state behavior in LTI systems, and how you can evaluate them with different inputs. ...
0
votes
1answer
2k views

How to determine the step response using convolution of the signal's impulse response?

The step response can be determined by recalling that the response of an LTI to any input signal is found by computing the convolution of that signal with the impulse response of the system. ...
0
votes
2answers
24 views

Mathematical Backing for Observations seen in Adding Independent Random Variables Together

So I have a function Y = F(N) that takes as an argument an integer number N and returns a summation of N sine-waves of different random parameters. I have plotted the results of two function calls ...
0
votes
0answers
10 views

Signal processing linear invariant causal systems

What is the frequency response of the linear invariant causal systems? I know that the response of linear invariant causal systems is g(k)=0 for k<0 but how about the frequency response?
0
votes
0answers
33 views

Fourier series for a Sinusoid in a conventional way?

So my TA in class introduced this amazing way of finding fourier series coefficients for a sin wave, by writing $ sin( \omega t ) = (e^{i\omega t}-e^{-i\omega t}) / 2i $ ----(1) Hence getting the ...
1
vote
1answer
541 views

How do I compute “AUC” Area under the curve number, if all I have are my TPR and FPR values?

I am trying to rank my neural network, which is trained for binary classification. That is, given a set of input signals, it outputs either a 1 or a 0. I have a training set, where I have the actual ...
0
votes
1answer
325 views

Matlab: Impulse response of linear time invariable (LTI) sine-signal

I'm preparing for a lab in a Signals and Systems course in my university, 5th semester. I've found old exercise material from the class and since I know some Matlab and have dealt with LTI systems ...
0
votes
1answer
59 views

confused with the FFT output

I am taking some sensor output and doing fft on it. how to get the exact frequencies from the complex output? my understanding is that bin frequencies and the input frequencies are different. Please ...
0
votes
0answers
13 views

How should I calculate a rolling autocorrelation?

I have an array of data $ \mathbf{y} \in \mathbb{R}^n $, and I need to calculate the lag-1 autocorrelation between sections of this array 7 elements long. For all intents and purposes, we can imagine ...
1
vote
4answers
74 views

Integrating unit impulse function

Given that, $$ \delta(t) = \begin{cases} \infty & \text{if } t = 0 \\ 0 & \text{if } t \ne 0\\ \end{cases}$$ How is it that, (A) $$ \int_{-\infty}^\infty \delta(t) dt = 1 $$ (B) $$ ...
8
votes
2answers
15k views

Integration of sawtooth, square and triangle wave functions

Context After a discussion about how to plot the results of a frequency modulation between two signals on Stack Overflow, I understood that I need to find the time-integral of the following wave ...
0
votes
1answer
33 views

Rewrite sinc function

I am working on an exercise in binary transmission systems. The pulses are modeled using a special sinc-function in the time-domain, $f_0$ is the bitrate but just a constant in time domain: $s(t) = ...
-1
votes
0answers
17 views

estimate the effective size of a gaussian?

How can I estimate the effective size of a gaussian? How bad is think that the size of the gaussian is twice its FWHM? Exist a better way of estimate this effective size?
1
vote
0answers
13 views

Change of Variable for Time Invariance Check

I've been studying for a signals and systems class coming this fall and can't figure out how the following change of variable is being applied according to standard definition: $$T[x(t-\sigma)] = ...
3
votes
1answer
388 views

Plotting discrete time signals involving sumations in matlab.

Many of the examples I've encountered while looking for an answer are simple functions that do not involve summations. Suppose I have the following function; ...
2
votes
1answer
52 views

Find $a$, given $y(n)=x(n)+ax(n-d)$, interesting question

Me and two friends of mine are working on a project (scholarly purposes only). The goal of this project is to clean an audio signal (speech, a song, anything audio) of echo. Generally speaking, if ...
0
votes
1answer
358 views

What is a moving average system?

Can someone elaborate on what a moving average system is? I know that the system is defined as: $$y[n] = \frac{x[n] + x[n-1] + x[n-2]}{3}$$ How would we draw $y[n]$ given that we have a graph with ...
0
votes
0answers
19 views

averaging of multiple curves for signal processing

I have response (vibration amplitude over frequency steps) measured over various point on my structure. In simpler way: i have 5 response curves(amplitude vs frequency plot) from same structure is ...
1
vote
1answer
53 views

Help needed with the integral of an infinite series

Can you please help me with the integral of this series? I came across it in a signal processing paper and haven't been able to figure out the solution myself. $$ ...
0
votes
0answers
22 views

Express the sum of squares as a percentage of how well two signals match?

So I am using matlab to compare two signals using the sum of squares. So the best possible match will be zero. eg $\sum(y_2 - y_1)$ where $y_2 = y_1$ would be $0$. The larger the sum of squared value ...
2
votes
1answer
380 views

Kalman Filter Process Noise Covariance

I want to model the movement of a car on a straight 300m road in order to apply Kalman filter on some noisy discrete data and get an estimate of the position of the car. In a Kalman filter the matrix ...
1
vote
1answer
35 views

How to calculate the partition function of a given distribution?

As noted in A FULL BAYESIAN APPROACH FOR INVERSE PROBLEMS, let $ y = Ax + n$, where $y$ is a $m$ dimensional signal and $n$ is white Gaussian noise with precision $\beta$, so we have: $$ y|x, \beta ...
3
votes
0answers
92 views

Is there a closed-form approximation to a band-limited sawtooth?

A partial Fourier Series with no coefficients is equal to the closed form expression: $${A \over n} \sum_{k=1}^n \cos(k\theta) = {A \over 2n} \left\{{\sin([2n + 1]\theta/2) \over \sin(\theta/2)} - ...
1
vote
1answer
16 views

Can an arbitrary real function be written in terms of quadratures of an arbitrary frequency with time dependent coefficients?

Given a real function $f$, and a frequency $\Omega$, is it the case that there exist two other real functions $I$ and $Q$ such that $f$ can be written as $$f(t) = I(t) \cos(\Omega t) - Q(t) ...
2
votes
0answers
34 views

Sampling a Chebyshev polynomial with the discrete cosine transform

I have a Chebyshev polynomial $f$ of degree $n$ in point-value form \begin{align} f&=:S = \left( \left( x_i, y_i \right) \right)_{i=0}^n, \tag{1} \\ x_i &= \cos\left( \frac{i \pi}{n} \right), ...
0
votes
2answers
69 views

Help needed with the integral of an infinite series

Can you please help me with the integral of this series? I came across it in a signal processing paper and haven't been able to figure out the solution myself. $$ ...
0
votes
0answers
18 views

DFT of subdomain of periodic domain

$f(t_i,x_j)$ is a solution of stochastic differential equation on grid. $j=[0,N+1]$, $i=[0,\infty]$ and boundary conditions are periodic: $f(t_i,x_0) = f(t_i,x_N)$ and $f(t_i,x_{N+1}) = f(t_i,x_1)$ ...
0
votes
0answers
60 views

Example of BIBO stable system that is not internally stable

In the theory of system, we know that a system can be BIBO stable but not internally stable (if there is a pole-zero cancellation in the transfer function for example). I find this concept quite ...
2
votes
1answer
34 views

Inverse-Fourier transform of a function after non-linear frequency modulation

Suppose $g\in L^1(\mathbb{R})$ such that $\hat{g}\in L^1(\mathbb{R})$ too. So $\tilde{g}(x) = \int_{-\infty}^{\infty}e^{i\pi \xi^2}\hat{g}(\xi)e^{2\pi i \xi x}\,d\xi$ is well-defined. Question is: Is ...
0
votes
1answer
42 views

Compressive sensing for complex matrix

I'm fairly new to compressive sensing, and I have been looking for a MATLAB implementation of the problem $$ A x = b $$ where $A$ is non square, $x$ is kind of sparse and all the numbers involved are ...
0
votes
0answers
12 views

How to apply a time shift to a pulse-shape, spanned with spline functions?

I have a sampled pulse shape: $ h = [1, 0.5]$ and I do not know what is its real underlying continuous-time pulse. I want to compute the samples of $h(t-\Delta t)$. If I write the continuous pulse ...
2
votes
0answers
32 views

Generating cross-correlated stochastic processes

I am looking for a robust way to represent and generate multiple stochastic processes that contain time and cross-correlations i.e. I am looking at stochastic processes $X_t^{1}$, $X_t^{2}$, $\ldots$, ...
0
votes
1answer
53 views

Using Product rule to take derivative

I'm trying to take the derivative of: $$\frac{-1}{6}(e^{-3t}-1) u(t)$$ The $u(t)$ is the step response. So the answer I get is by just doing product rule: ...
3
votes
1answer
153 views

Artifacts and low frequencies FFT.

I am working on analyzing a time signal and want to preform a FFT. However I run in to some artifacts at low frequencies. I have managed to reproduce the behavior in a test signal. Given by $S(t) = ...
1
vote
0answers
24 views

How to decorrelate/Whiten a non-white additive random variable?

I have a signal processing problem where I have the Additive Noise Model (assume Gaussian noise). $$ y = x + w $$ where, $y$ is corrupted signal, $x$ is original signal & $w$ is a non-white ...
3
votes
0answers
38 views

Looking for Math books recommendations to study Electronics

My background is the very basics, and I mean, literally, I can add, sub,mul,div and a little of algebra (near, nothing) and that's it. As you can see I need the best Total Beginner Book(s) that can ...
1
vote
2answers
60 views

How does one verify if a vector is really recovered?

In compressed sensing, how to verify if a vector is really recovered or how does one plot the figures on recovery rate? Since in numerical experiments, there is always a difference between the ...
2
votes
2answers
42 views

Inversion of the Burrows Wheelers Transform

The "Burrows-Wheeler Transform" in signal processing is a transformation which is used in for instance data compression and pattern recognition. It can be described in mathematical terms as: Start ...
1
vote
2answers
232 views

Can the measurement matrix used for compressive sensing be a sparse matrix?

I am interested in analyzing Compressive Mechanism: Utilizing Sparse Representation in Differential Privacy. In my research, the measurement matrix $A\mathbb \in R^{m \times n}$ needs to be sparse. ...